Enabling Privacy-Preservation in Decentralized Optimization

Decentralized optimization is crucial for the design, deployment, and functionality of many distributed systems. In this paper, we address the problem of privacy-preservation in decentralized optimization. In most existing decentralized optimization approaches, participating agents exchange and disclose intermediate estimate values to neighboring agents explicitly, which may not be desirable when the estimates contain sensitive information of individual agents. The problem is more acute when adversaries exist which try to steal information from other participating agents. To address this issue, we propose a novel approach that enables privacy-preservation in decentralized optimization by combining partially homomorphic cryptography with the unique properties of the decentralized optimization. We show that cryptographic techniques can be incorporated in a fully decentralized manner to enable privacy-preservation in decentralized optimization in the absence of any third party or aggregator. This is significant in that to our knowledge, all existing cryptographic-based optimization approaches rely on the assistance of a third-party or aggregator in order to protect the privacy of all parties. The approach is also applicable to the average consensus problem, which is finding broad applications in fields as diverse as robotic networks, distributed computing, and power systems. Numerical simulations confirm the effectiveness and low computational complexity of the proposed approach.